A PROOF OF BEAL'S CONJECTURE

It is proved in this paper t that the equation $z^\xi=x^\mu+y^\nu$ has no solution in relatively prime positive integers $x, y, z,$ with $\xi, \mu, \nu$ odd primes at least $3.$ This is equivalent to Fermat\rq{}s Last Theorem which is stated as follows: If $x.y, z$ are positive integers, and $\pi$ is an odd prime satisfying $z^\pi=x^\pi+y^\pi,$ then $x, y, z$ are not relatively prime.